In conjunction with linear general integral control, this paper proposes a fire-new control design technique, named Equal ratio gain technique, and then develops two
kinds of control design methods, that is, Decomposition and Synthetic methods,
for a class of uncertain nonlinear system. By Routh’s stability criterion, we demonstrate
that a canonical system matrix can be designed to be always Hurwitz as any row
controller gains, or controller and its integrator gains increase with the same
ratio. By solving Lyapunov equation, we demonstrate that as any row controller
gains, or controller and its integrator gains of a canonical system matrix tend
to infinity with the same ratio, if it is always Hurwitz, and then the samerow solutions of Lyapunov equation all
tend to zero. By Equal ratio gain technique and Lyapunov method, theorems to
ensure semi-globally asymptotic stability are established in terms of some
bounded information. Moreover, the striking robustness of linear general
integral control and PID control is clearly illustrated by Equal ratio gain technique.
Theoretical analysis, design example and simulation results showed that Equal
ratio gain technique is a powerful tool to solve the control design problem of uncertain
nonlinear system.

Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Linear System Theory. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, 5, 3174-3177.

Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Sliding Mode Technique. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, 5, 3178-3181.

Liu, B.S. (2014) On the Generalization of Integrator and Integral Control Action. International Journal of Modern Nonlinear Theory and Application, 3, 44-52. http://dx.doi.org/10.4236/ijmnta.2014.32007